Relationship Expert Julia Allison's Non-Negotiable: Must Love Dogs

After years on the scene, dating columnist Julia Allison has developed a list of things she's looking for in a mate – a 73-point checklist, to be exact.

"Loves me unconditionally" is at the top – and yes, 30-year-old Allison is still looking for The One – but among her non-negotiables? "Must love animals, especially Lilly."

Lilly (who has her own Twitter page is Allison's 9-year-old Shih Tzu, and the two have been together since Allison's senior year at Georgetown University, where she ignored the rules and brought a pet into her dorm room. They've been attached ever since, and are costars of sorts on Bravo's new reality show about three single relationship experts, Miss Advised.

"She's so great with people because I used to take her to bars and frat parties," Allison tells PEOPLE. "She's a very California dog. She has more the personality of a cat, or a dog on a heavy dose of medical marijuana. She's very sweet."

Lilly acts as a natural barometer for Allison's prospective boyfriends. Over the years, she has liked some men more than others, and has even barked at some. "If I trust you with my dog, that's a really good sign for our relationship," Allison says.

She has advice for other single pet lovers out there: "You want to look at how someone treats your animal," she says. "It's like what they say about how a person treats a waiter or waitress: that's how they'll treat you eventually. So if they treat your animal with kindness and respect, that's the way they'll be with you – and, with your kids one day."